Orbital Stark effect and quantum confinement transition of donors in silicon

Abstract

Adiabatic shuttling of single impurity bound electrons to gate-induced surface states in semiconductors has attracted much attention in recent times, mostly in the context of solid-state quantum computer architecture. A recent transport spectroscopy experiment for the first time was able to probe the Stark shifted spectrum of a single donor in silicon buried close to a gate. Here, we present the full theoretical model involving large-scale quantum mechanical simulations that was used to compute the Stark shifted donor states in order to interpret the experimental data. Use of atomistic tight-binding technique on a domain of over a million atoms helped not only to incorporate the full band structure of the host, but also to treat realistic device geometries and donor models, and to use a large enough basis set to capture any number of donor states. The method yields a quantitative description of the symmetry transition that the donor electron undergoes from a three-dimensional Coulomb confined state to a two-dimensional ͑2D͒ surface state as the electric field is ramped up adiabatically. In the intermediate field regime, the electron resides in a superposition between the atomic donor states and the 2D surface states. In addition to determining the effect of field and donor depth on the electronic structure, the model also provides a basis to distinguish between a phosphorus and an arsenic donor based on their Stark signature. The method also captures valley-orbit splitting in both the donor well and the interface well, a quantity critical to silicon qubits. The work concludes with a detailed analysis of the effects of screening on the donor spectrum.

Highly tunable exchange in donor qubits in silicon

“…22 All these works are based on the Kohn-Luttinger form of the donor wavefunctions, 23 which provides a very specific solution to the two-electron problem, and cannot provide a full description of the (1,1) to (2,0) charge transition in which strong Stark effect causes mixing of the lowest states with many excited states. 18 The atomistic configuration interaction method used here goes beyond these approximations to include the Stark effect, large wavefunction overlap and electron-electron exchange and correlations. In this work, we use a large-scale atomistic tight-binding method that describes the crystal as a linear combination of atomic orbitals, and captures the full-energy spectrum of a donor in silicon, including the conduction band valley degrees of freedom, the valley-orbit interaction, 24 the Stark shift of the donor orbitals, 18 and real and momentum space images of the donor obtained by scanning tunnelling microscope experiments.…”

“…18 The atomistic configuration interaction method used here goes beyond these approximations to include the Stark effect, large wavefunction overlap and electron-electron exchange and correlations. In this work, we use a large-scale atomistic tight-binding method that describes the crystal as a linear combination of atomic orbitals, and captures the full-energy spectrum of a donor in silicon, including the conduction band valley degrees of freedom, the valley-orbit interaction, 24 the Stark shift of the donor orbitals, 18 and real and momentum space images of the donor obtained by scanning tunnelling microscope experiments. 25 Using the atomistic wavefunctions, we compute the two-electron states of donor and donor clusters in the presence of an electric field from an FCI technique.…”

“…In our simulations with uniform electric fields, we are unable to go to the high-field regime for the 1P-1P case, as high fields induce a triangular quantum well at the lateral domain boundaries causing electron localisation in the surface states. 18 However, larger exchange energies can possibly be realised even in the 1P-1P case with large spatially varying E-fields from detuning gates as shown in Figure 1b,c. In Supplementary Information, we show that the exchange coupling of a 1P-1P system can be tuned by a factor of 50 using surface-detuning gates.…”

Hyperfine Stark effect of shallow donors in silicon

“…For these reasons, the Stark effect in doped silicon has been broadly studied in literature, either theoretically [14][15][16][17][18][19][20][21][22] or experimentally [23,[25][26][27][28]. More generally, the ability to theoretically describe the donor electron wave function accurately in a wide range of electrostatic environments is beneficial for determining the values of control parameters which provide best performance, and in the best case for estimating a priori the feasibility of quantum algorithms and error correction codes [20].…”

A computational workflow for designing silicon donor qubits

“…Tight-binding (TB) [36,37] and densityfunctional tight binding (DFTB) [38] methods that make use of these approximations are computationally attractive alternatives for electronic structure modeling of silicon donor qubit devices. Whereas TB methods have been used extensively for modeling silicon donor systems [31,32,[39][40][41][42][43], DFTB methods have not yet been extensively applied.…”